How do neutrons keep protons together in an atom’s core if they don’t have a charge?

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Wouldn’t it make more sense if neutrons had a negative charge so the protons would be attracted towards it? Is it just the neutrons mass that keeps the protons together?

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There are four fundamental forces of the universe: electromagnetism, gravity, and the strong and weak nuclear forces. You have considered magnetism and gravity, but not the other two.

The answer to your question is the Strong Nuclear Force. It keeps the nucleus of atoms bound to each other.

The strong nuclear force is what holds the nucleus together

This is a separate force from the Electromagnetic Force which is what you think of with Positive and Negative charges.

The strong force is very strong as the name implies, but it is very short range. So it can only take effect within the nucleus.

Even a very short distance away from the nucleus the Electromagnetic force is stronger, which is what causes the Protons to repel each other. Only in the heart of a star is their enough energy for the Protons to come close enough to overpower EM and fuse together. Once 2 Protons fuse one of them becomes a neutron and releases energy as a positron and a neutrino.

Lone Neutrons meanwhile have a half life of 10.3 minutes and will decay into Protons via neutron beta decay

Strong force acts to keep them together, but this alone isn’t sufficient, so neutrons provide that little bit of extra spacing to keep things *just* far enough apart that EM won’t eject them from the corr, but *just* close enough that the strong force can keep them bound up. This is why the largest of atoms are radioactive (the balance is so precise that any stray wiggle will break the balance and cause Things To Happen). Or at least, that’s my head Canon for how it works. I could be totally off. What I do know is that they are essential.